报告题目：On tetravalent half-arc-transitive graphs
报告人：周进鑫 教授
报告时间：2025年11月7日 16:30-17:30
报告地点：科技园阳光楼南815
邀请人：范更华
邀请单位：91视频
、离散数学及其应用省部共建教育部重点实验室
报告摘要：Vertex-stabilizers of trivalent edge-transitive graphs have been classified by Tutte, Goldschmidt and some others in several previous papers. Tetravalent half-arc-transitive graphs form an important class of tetravalent edge-transitive graphs. Maru\v si\v c and Nedela (2001) initiated the study of the problem of classifying vertex-stabilizers of tetravalent half-arc-transitive graphs, which has received extensive attention and considerable effort in the literature. In this talk, I will introduce some progress on this problem. We first give a solution of this problem by proving that a group is the vertex-stabilizer of a connected tetravalent half-arc-transitive graph if and only if it is a non-trivial concentric group. Then we give an explicit construction of an infinite family of tetravalent half-arc-transitive graphs with automorphism group isomorphic to $A_{2^n}\wr \mz_2$ and vertex-stabilizers isomorphic to $(D_8^2\times\mz_{2}^{n-6})^2$ for $n\geq7$. These are the first known family of basic tetravalent half-arc-transitive graphs of bi-quasiprimitive type.
报告人简介：周进鑫，北京交通大学91视频
教授，博导，国家自然科学基金杰出青年基金获得者。主要从事对称图论研究。在组合数学、图论、代数等领域权威期刊Journal of Combinatorial Theory, Series A/B, Combinatorica, European Journal of Combiatorics, Journal of Graph Theory, Journal of Algebra, Journal of Algebraic Combintorics等上发表论文100余篇。主持和参与国家自然科学基金等科研项目10余项。
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